### Five Quickies

#### Posted by Tom Leinster

I’m leaving tomorrow for an “investigative workshop” on Information and Entropy in Biological Systems, co-organized by our own John Baez, in Knoxville, Tennessee. I’m excited! And I’m hoping to learn a lot.

A quick linkdump before I go:

**Reflexive completion**Tom Avery and I are writing a paper on Isbell conjugacy and reflexive completion (also called Isbell or MacNeille completion). I gave a talk on it last week at the British Mathematical Colloquium in Cambridge, which is somewhat similar to the Joint Meetings in the US.The concepts of Isbell conjugacy and reflexive completion are at the same

*very*basic, primitive categorical level as the Yoneda lemma. They rely on nothing more than the notions of category, functor and natural transformation. But they’re immeasurably less well-known than the Yoneda lemma.As for Tom, you may remember him from the Kan Extension Seminar. He’s doing a PhD with me here in Edinburgh.

**Mathematicians accepting and resisting overtures from GCHQ**The British Mathematical Colloquium was part-sponsored by the UK surveillance agency GCHQ, which I’ve written about many times before. They paid for one of the plenary talks and some of the costs of student attendance. (They didn’t pay for me.)I began my talk by expressing both my thanks to the organizers and my disappointment in them for allowing an extremist organization like GCHQ to buy itself a presence at the conference. As I understand it, the deal was that in return for the money it paid, GCHQ got a recruiting platform for the Heilbronn Institute (their academic brand). For instance, the conference hosted a Heilbronn recruitment session, advertised in the blurb that every delegate received.

And I said that although one might think it irregular for me to be taking a few moments of my seminar to talk about this, consider the fact that GCHQ bought itself three whole days in which to create the impression that working for an agency of mass surveillance is a normal, decent thing for a mathematician to do.

There were several encouraging signs, though:

- An important person within the organizational structure of the British Mathematical Colloquium (an annual event) exhibited clear awareness that GCHQ involvement in the BMC was controversial. This is a start, though it requires people to keep pointing out that committees, as well as individuals, are making a political choice when they cooperate with the intelligence agencies.
- The conference website advertised that GCHQ would have a stand/booth at the conference, but in the end they didn’t — perhaps knowing that they’d have been asking for trouble.
- I heard that a certain prominent British mathematician had refused requests to review from both GCHQ and the NSA.
- And as usual, just about every mathematician I spoke to was opposed to GCHQ mass surveillance.

**The Euler characteristic of an algebra**I recently gave a couple of talks entitled “The Euler characteristic of an algebra”: one for category theorists and one for algebraists. This represents joint work with Joe Chuang and Alastair King, which I hope we’ll have written up soon. I wrote a couple of posts warming up to this result, though I never got round to the result itself.**Review of Nick Gurski’s higher categories book**I wrote a review of Nick Gurski’s book*Coherence in Three-Dimensional Category Theory*. The review will appear in the*Bulletin of the London Mathematical Society*.**Are lectures the best way to teach?**Nick also has an opinion piece in*The Guardian*(joint with his colleague Sam Marsh), answering the question: are lectures the best way to teach students?

## Re: Five Quickies

Just a reply to your first and last point.

I look forward to talking to you and Tom about reflexive completions. I’m in Honolulu talking to Dusko Pavlovic about related things.

As for your last point, I was involved in the project with Nick and Sam. Just before I came over to Hawaii, we were down in London at the Guardian University Awards, where we were runners up in the Teaching Excellence category. You don’t see Nick or me with a tie on very often, but here’s a picture of us at the awards ceremony.

Sam and Nick are on the left. The chap in the middle is Sheffield MP Paul Bloomfield who got the Most Inspiring Leader in Higher Education award. The chap on the right is Tony Ryan, our Pro-Vice Chancellor for Science (the equivalent of a Dean).